Preheat the oven to 400 degrees . In a large skillet, steam the corned beef in 1/4 cup water over medium heat until warmed through, about 4 minutes.
Meanwhile, in a small bowl, combine the ketchup, mayonnaise and relish.
Working on a baking sheet, spread the dressing onto one side of each bread slice. Divide the corned beef among the bread slices and top with the sauerkraut. Top with the cheese. Bake until the cheese is melted, about 5 minutes.